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	Genus Information - TextSheet.com
		In biology, a genus (plural genera) is a grouping in the classification of living organisms having one or more related or morphologically similar species.
		The specimen used to describe this species is kept as the holotype in a zoological museum or a herbarium to be available for further study.
		A genus name in one kingdom is allowed to be the same as a genus or other taxon name in another kingdom.
	www.medbuster.com /encyclopedia/g/ge/genus.html (260 words)

	Genus - Encyclopedia.WorldSearch (Site not responding. Last check: 2007-10-21)
		The type genus of a taxon is usually the first genus to be named and described.
		The genus and these higher taxa are typified by a specimen that shows the characteristics of the genus.
		For instance, Anura is a genus of plants as well as the order of frogs; Aotus is both a pea and a monkey; Oenanthe and Oenanthe are genera of birds and plants respectively, as are Prunella and Prunella.
	encyclopedia.worldsearch.com /genus.htm (388 words)

	Mathematics
		Mathematics 3 and 8 cover the basic calculus of functions of a single variable, as well as vector geometry and calculus of scalar-valued functions of several variables.
		Prerequisite: Mathematics 8, or Mathematics 3 and 6.
		The mathematical methods of Mathematics 6, or Mathematics 20, and Mathematics 13 are extended and applied to the study of mathematical models developed for use in such fields as anthropology, biology, economics, sociology, psychology, and linguistics.
	www.dartmouth.edu /~reg/courses/desc/math.html (7640 words)

	Genus -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-21)
		See (Click link for more info and facts about genus (mathematics)) genus (mathematics) for the use of the term in (A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement) mathematics.
		In (The science that studies living organisms) biology, a genus (plural genera) is a grouping in the classification of living organisms having one or more related and (Click link for more info and facts about morphologically) morphologically similar ((biology) taxonomic group whose members can interbreed) species.
		The ((biology) genus from which the name of a family or subfamily is formed; it is not necessarily the most representative genus but often the largest or best known or earliest described) type genus of a (Animal or plant group having natural relations) taxon is usually the first genus to be named and described.
	www.absoluteastronomy.com /encyclopedia/g/ge/genus.htm (544 words)

	Handle (mathematics) - Wikipedia, the free encyclopedia
		In topology, a branch of mathematics, a handle is just a topological ball; it is called a handle because of the context in which it is discussed, of which there are two: handle decompositions and handlebodies.
		A handle is a subset of a manifold built up (or decomposed) by handle decomposition.
		A handle is a subset of a handlebody; a handlebody of genus n will have n handles.
	en.wikipedia.org /wiki/Handle_(mathematics) (94 words)

	Algebraic curves (Site not responding. Last check: 2007-10-21)
		The genus of a connected, oriented surface is an integer representing the maximum number of cuttings along closed simple curves without rendering the resultant manifold disconnected.
		The genus of a knot of a knot (mathematics) K is defined as the minimal genus of all Seifert surfaces for K. The genus of a 3-dimensional handlebody is an integer representing the maximum number of cuttings along embedded Disk (mathematics) without rendering the resultant manifold disconnected.
		There is a definition of genus of any algebraic curve C. When the field of definition for C is the complex numbers, and C has no tangent space, then that definition coincides with the topological definition applied to the Riemann surface of C (its manifold of complex points).
	read-and-go.hopto.org /Algebraic-curves (248 words)

	Aristotle and Mathematics
		Mathematical examples: ‘line’ is in the definition of triangle, ‘point’ is in the definition of line.
		The objects studied by mathematical sciences are perceptible objects treated in a special way, as a perceived representation, whether as a diagram in the sand or an image in the imagination.
		The parts of a mathematical object which do not occur in the definition of the object, e.g., acute angle is not in the definition of right angle, but is a part of it and so is a non-perceptible material part of the angle (Metaphysics vii.10, 11).
	plato.stanford.edu /entries/aristotle-mathematics (9454 words)

	Algebraic curve - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-21)
		In the Riemann surface case that is the same as the topologist's idea of genus of a 2-manifold.
		The genus enters into the statement of the Riemann-Roch theorem and can be characterized as the only integer that makes this theorem correct.
		The case of genus 1 - elliptic curves - has in itself a large number of deep and interesting features.
	xahlee.org /_p/wiki/Algebraic_curve.html (295 words)

	Genus - LearnThis.Info Enclyclopedia (Site not responding. Last check: 2007-10-21)
		See genus (mathematics) for the use of the term in mathematics.
		See genus (music) for the use of the term in music.
		A genus name in one kingdom is allowed to bear the same name as a genus or other taxon name in another kingdom.
	encyclopedia.learnthis.info /g/ge/genus.html (323 words)

	[No title]
		An independent proof of Notbohm's theorem on the classification of the adic genus of BS3 by KO-theory ~-rings is given.
		For a nilpotent finite type space X, we denote by Genus (X), call the adic genus of X, the set of homotopy types of nilpotent finite type spaces Y such that the p-completions of X and Y are homotopy equivalent for each prime p and also their rationalizations are homotopy equivalent.
		Genus (X), Q where X^0is the rationalization of the formal completion X^= pX^pof X. Notice that each homotopy group ß*(X^0) is a Q bZ-module, and Caut(X^0) is by definition the group of homotopy classes of self-homotopy equivalences of X^0whose induced maps on homotopy groups are Q bZ-module maps.
	hopf.math.purdue.edu /YauD/adic_genus2.txt (4839 words)

	Genus \| TutorGig.co.uk - The Tutorial Website (Site not responding. Last check: 2007-10-21)
		genus mathematics for the use of the term in mathematics.
		In biology..." >Genus, genus has few different, but closely related, meanings Topology Orientable surface The genus of a connected, orientable surface is an integer representing the maximu..." >Genus (mathematics), Genus50f.JPG right thumb Cover of Genus 50.
		genus - creatures wiki genus from creatures wiki the genus is part of the classification system in use....
	www.tutorgig.co.uk /searchtgig.jsp?keywords=Genus (641 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		They must, of course, have the same genus, but there must also be a 1-1 and onto function from one to the other that is everywhere analytic, with an analytic inverse.
		But for higher genus there are infinitely many essentially different ways to give a surface of genus g a complex structure.
		Define the mapping class group (of genus g) to be the group of diffeomorphisms of a surface of genus g modulo the subgroup of those connected to the identity.
	math.ucr.edu /home/baez/twf_ascii/week28 (2194 words)

	Research & Grant Activities (Site not responding. Last check: 2007-10-21)
		The active research by members of the Mathematics Department faculty falls into five broad categories; Algebra and Geometry, Analysis, Applied Mathematics, Mathematics Education, and Probability and Statistics.
		The Mobile Mathematics Initiative (MMI) is a collaborative effort between the Mobile Area Education Foundation, the University of South Alabama, and the professional development team, led by Dr. Bamberger.
		Mathematics and culture: a minicourse from the February 2001 focus issue of Teaching Children Mathematics (co-organizer), Annual Meeting of the National Council of Teachers of Mathematics, Orlando, Florida, April 2001.
	www.towson.edu /~math/about_the_faculty/research_grant.html (3526 words)

	Recent preprints by Marston Conder (Site not responding. Last check: 2007-10-21)
		Even in pure mathematics, where often quite subtle and sophisticated arguments are required for the solution of problems, computers have become an invaluable, almost indispensible tool.
		We show that it is possible to have genus range equal to 1, with arbitrarily large (minimum) genus, unlike in the undirected case.
		Complete lists are given of all reflexible orientable regular maps of genus $2$ to $15$, all non-orientable regular maps of genus $4$ to $30$, and all (orientable) rotary but chiral (irreflexible) maps of genus $2$ to $15$ inclusive.
	www.scitec.auckland.ac.nz /~conder/preprints (2743 words)

	Amazon.ca: Books: Integrable Systems and Riemann Surfaces of Infinite Genus (Site not responding. Last check: 2007-10-21)
		Their spectral curves, i.e., the common spectrum with the periodic shifts, are generically Riemann surfaces of infinite genus.
		These line bundles may be described by divisors of the same degree as the genus, and these divisors give rise to Darboux coordinates.
		With the help of a Riemann-Roch Theorem, the isospectral sets (the sets of all potentials corresponding to the same spectral curve) may be identified with open dense subsets of the Jacobian varieties.
	www.amazon.ca /exec/obidos/ASIN/082180460X (336 words)

	Encyclopedia: FOX
		Species Urocyon cinereoargenteus Urocyon littoralis The genus Urocyon contains two Western Hemisphere members of the fox family, the Gray Fox (Urocyon cinereoargenteus) and the closely related Island Fox (Urocyon littoralis), of the family Canidae.
		Binomial name Urocyon littoralis (Baird, 1857) The Island Fox (Urocyon littoralis) is a small fox that is native to six of the eight Channel Islands of California.
		Species Vulpes bengalensis Vulpes cana Vulpes chama Vulpes corsac Vulpes ferrilata Vulpes macrotis Vulpes pallida Vulpes ruppelli Vulpes velox Vulpes vulpes Vulpes zerda Vulpes is a genus of the Canidae family.
	www.nationmaster.com /encyclopedia/FOX (2126 words)

	Philolaus and Euclid
		For the diatonic genus, the interval was tuned to various “major tones,” for the chromatic genus, to various “minor thirds,” and for the enharmonic genus, to various “major thirds.” Figure 1 shows a typical tetrachord for each genus.
		The earliest known mathematical description of a systematic canon tuning is contained in a work entitled Division of the Canon, reputedly written by Euclid (fl.
		However, such a procedure would have violated the practice of defining the genus of a given tetrachord by tuning the characteristic interval as an interval that descends from the fourth tone to the third tone of the tetrachord.
	www.chrysalis-foundation.org /Philolaus_&_Euclid.htm (3187 words)

	[No title]
		Algorithm 3.2 Input: A non-splittable imbedding I(H'g) of H'g in G Output: A subgraph H"g of G, an imbedding I(H"g) of H"g of genus g and a minimal set R of bridges of G-H"g that cannot be all imbedded onto I(H"g) without increasing the genus.
		Algorithm 4.2 Input: I(H), a weakly quasiplanar imbedding regarding G Output: Imbedding of G of the same genus as I(H), if I(H) is extendible to G, or a path p in K whose vertices correspond to a forbiddeng set C of bridges 1.
		Informally, a closed surface of genus g consists of a sphere with the addition of g handles.
	www.cs.duke.edu /~reif/paper/djidjev/genus.doc (4676 words)

	The Mobile Collection (Graphics) (Site not responding. Last check: 2007-10-21)
		It is a random collection of surfaces with close connection to Hermann Karcher's work, each surface selected by mathematical as well as aesthetical criteria.
		Lawson constructs compact minimal surfaces in the 3-sphere of arbitrary genus by applying Morrey's solution of the Plateau problem in general manifolds.
		The Genus-One Helicoid is a minimally embedded torus with one end and infinite total curvature.
	www.math.uni-bonn.de /people/karcher/Mobile_Graphics.htm (565 words)

	Jay Zimmerman (Site not responding. Last check: 2007-10-21)
		The symmetric genus of finite abelian groups (with Coy L. May) Illinois J. of Math., Vol.
		The symmetric genus of metacyclic groups (with Coy L. May), Topology and its Applications, 66, (1995), 101-115.
		The symmetric genus of groups of odd order (with Coy L. May), submitted to the Houston Journal of Mathematics.
	www.towson.edu /~zimmer/zim.htm (239 words)

	[No title]
		I prefer working on problems in an environment where a blend of analysis and computation is preferred (as opposed to throwing all available hardware at a situation without thinking about it, or coming up with purely abstract theoretical results).
		Dissertation: On the projective geometry of curves of genus one, and an algorithm for the jacobian of such a curve.
		I studied mathematics and japanese at Tsukuba University, Tsukuba, Japan.
	math.arizona.edu /~aprl/cv/cv_AlexPerlis_2004-07-25.txt (981 words)

	Christopher French's Research (Site not responding. Last check: 2007-10-21)
		For one, group actions arise naturally both in physics and in mathematics, and understanding these actions can be used to help compute a variety of invariants in both fields.
		When a finite group G acts on a manifold M, the quotient M/G is an orbifold, and one can associate to M/G an orbifold string genus in physics and an orbifold elliptic genus in mathematics.
		In physics, there is a degree of freedom in defining the orbifold string genus, called discrete torsion, and this indeterminacy is parametrized by elements in H^3(G;Z), the third cohomology of the group G. Ando and I have found a feature in mathematics with remarkably similar properties.
	www.math.grin.edu /~frenchc/Research (435 words)

	Mathematics of Computation
		The first algorithm, inspired by Cantor's reduction for hyperelliptic curves, is easily implemented with a few lines of code, making use of a polynomial arithmetic package.
		We prove explicit reducedness criteria for superelliptic curves of genus 3 and 4, which show the correctness of the algorithm.
		English translation in the proceedings of the Conference on The Mathematics of Public Key Cryptography, Toronto 1999.
	www.ams.org /mcom/2005-74-249/S0025-5718-04-01699-0/home.html (686 words)

	Proving That A Genus 2 Curve Has Complex Multiplication - van Wamelen (ResearchIndex) (Site not responding. Last check: 2007-10-21)
		Recently examples of genus 2 curves defined over the rationals were found which, conjecturally, should have complex multiplication.
		Introduction In [5] 18 non-trivial genus 2 curves defined over the rationals are given and it is conjectured that these curves have complex multiplication.
		That is, compute such an isogeny numerically to high precision and then guess the exact values for the coefficients of this morphism....
	citeseer.ist.psu.edu /vanwamelen97proving.html (375 words)

	SLU Mathematics Department ~ 2004-2005 Colloquium
		The goal of the textbook and the course is to present the mathematics clearly and correctly while keeping the focus on material that elementary school teachers will be addressing in their classrooms.
		The minimal genus problem deals with the minimal genus among all representatives of a given homology class in a four-manifold.
		Visual representations of the mathematics involved are provided, along with open problems in the subject of book embeddings.
	www.selu.edu /Academics/Depts/Math/coll04-05.html (1350 words)

	Jianer Chen's Publication List
		Chen, J., ``A linear-time algorithm for isomorphism of graphs of bounded average genus,'' SIAM Journal on Discrete Mathematics 7, pp.
		Chen, J. and Gross, J. ``Kuratowski-type theorems for average genus,'' Journal of Combinatorial Theory, Series B 57, pp.
		Chen, J. and Gross, J. ``Limit points for average genus I: 3-connected and 2-connected simplicial graphs,'' Journal of Combinatorial Theory, Series B 55, pp.
	faculty.cs.tamu.edu /chen/pub.html (3927 words)

	Summa Theologica (Site not responding. Last check: 2007-10-21)
		Objection 1: It seems that "one" adds something to "being." For everything is in a determinate genus by addition to being, which penetrates all "genera." But "one" is a determinate genus, for it is the principle of number, which is a species of quantity.
		For if a thing were "one" by anything else but by its substance, since this again would be "one," supposing it were again "one" by another thing, we should be driven on to infinity.
		Hence we must adhere to the former statement; therefore we must say that the "one" which is convertible with "being," does not add a reality to being; but that the "one" which is the principle of number, does add a reality to "being," belonging to the genus of quantity.
	www.ccel.org /a/aquinas/summa/FP/FP011.html (2382 words)

	Aquinas: Summa Theologiae (excerpt, part 3)
		But things not in the same genus are not comparable; as, sweetness is not properly greater or less than a line.
		Now the likeness of an effect in the univocal cause is found uniformly; but in the equivocal cause it is found more excellently, as, heat is in the sun more excellently than it is in fire.
		Now we say that God is not in the same genus with other good things; not that He is any other genus, but that He is outside genus, and is the principle of every genus; and thus He is compared to others by excess, and it is this kind of comparison the supreme good implies.
	praxeology.net /summa3.htm (3828 words)

	SIDMA Volume 9 Issue 1
		This paper develops new techniques for constructing separators for graphs embedded on surfaces of bounded genus.
		For any arbitrarily small positive $\varepsilon $ we show that any $n$-vertex graph $G$ of genus $g$ can be divided in $O(n + g)$ time into components whose sizes do not exceed $\varepsilon n$ by removing a set $C$ of $O(\sqrt {(g + 1/\varepsilon)} n)$ vertices.
		Our result improves the best previous ones with respect to the size of $C$ and the time complexity of the algorithm.
	locus.siam.org /SIDMA/volume-09/art_0409012.html (184 words)

	A Beautiful Mind
		He is a little eccentric, obsessive about his work and finds it hard to relate to his fellow students on a social level.
		This drama is based on the true-life story of mathematics genus Dr. John Nash who produced revolutionary maths theories but has to battle with the curse of schizophrenia.
		If, like me, the mere mention of figures has you reaching for the calculator don’t worry as the film is about the person and not the mathematics.
	www.premiermoviereviews.com /a_beautiful_mind.htm (407 words)

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